I was solving a problem that uses the fact: $1^3+2^3+\dots+n^3=(1+2+\dots+n)^2$. I know that this can be proved by induction or using $1^3+2^3+\dots+n^3=\left\{\frac{(n(n+1)}{2}\right\}^2$. But I am interested in visual proofs.
One idea to prove this visually is to show that the sum of the volumes of the cubes with side lengths $1,2,3,\dots,n$ equals to the area of a square with side length $(1+2+3+\dots+n)$. This idea also appeared in this answer which checks the validity of the idea just for small cases. So, completing this idea or some other ideas to prove this visually is highly appreciated.
(The question on finding a proof of the statement has already been asked here and here. But I didn't find any visual proof apart from the one I mentioned.)
